A COMMUTATOR RIGIDITY FOR FUNCTION GROUPS AND TORELLI’S THEOREM

A Trace-class Rigidity Theorem for Kleinian Groups

Suppose that ? 1 and ? 2 are geometrically nite, convex co-compact, discrete groups of isometries of real hyperbolic space H 3 whose domains of discontinuity are diieomorphic. We show that if the respective scattering matrices S 1 (s) and S 2 (s) diier from each other by a trace-class perturbation on the unitary axis Re(s) = 1, then ? 1 and ? 2 are conjugate in PSL(2; C). This result reeects th...

A Bowen type rigidity theorem for non-cocompact hyperbolic groups

We establish a Bowen type rigidity theorem for geometrically finite actions of the fundamental group of finite volume noncompact hyperbolic manifolds (with dimension at least 3). Mathematics Subject Classification (2000). 53C24, 30F40, 37F30.

A Rigidity Theorem for the Solvable Baumslag-solitar Groups

A Rigidity Theorem for Convex Surfaces

Theorem 1. Let (S2, g) be the two dimensional sphere with a metric of class C1,1 whose Gaussian curvature satisfies 0 ≤ K ≤ 1. Then any simple closed geodesic γ on (S2, g) has length at least 2π. If the length of γ is 2π, then (S2, g) is isometric to the standard round sphere (S2, g0) and γ is a great circle on (S2, g0) or (S 2, g) is isometric to a circular cylinder of circumference 2π capped ...

A rigidity theorem for L-theory

This paper was written in October, 1983, but never published. I am making it available on the internet in this form as a response to the requests for copies of the preprint received in the intervening years. As long as these servers are running, a dvi file of this paper will be available by gopher at gopher.math.uwo.ca and on the world wide web at http://www.math.uwo.ca. Only very minor changes...